Goal difference means nothing if you don't have the points on the board to make it count.
Leicester have already lost 20 games - a shocking statistic - this season, won only seven, and drawn a mere four. The only team that have been worse worse - and they have also been defeated on 20 occasions - is Southampton.
Each and every other team threatened by relegation have lost either 15 or sixteen games; at this stage, that is a big difference between them and the bottom two.
On their current form - which is dire - where can they expect to find the points to climb up a place or two? (Okay, pull a point back from a team such as Arsenal.....)
I don't think that Leicester's goal difference makes any difference at all, unless they start putting a few results togetehr, and time is running out for them.
Now, I will concur with you on the third and final trapdoor slot; there, yes, GD could well come into play, especially if there is a bunched clump, or cluster, of teams threatened with relegation as we come into the last day of the season.